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James H. Christenson, James Watson Cronin, Val Logsdon Fitch and René Turlay reported the result in 1964. At Brookhaven's AGS, 30 GeV protons struck beryllium; collimators selected a neutral particle beam at 30 degrees. A downstream helium decay volume reduced interactions.^[ref]

The flight distance suppressed the short-lived kaon component. Each arm of a two-arm magnetic spectrometer had spark chambers before and after its magnet. Cherenkov detectors and scintillation counters triggered photographic recording in coincidence.^[ref]

The helium sample yielded $45\pm 9$ signal events; $(2.0\pm 0.4)\times 10^{-3}$ was the ratio to all charged decay channels.^[ref] That denominator must be retained when comparing this result with a total branching fraction.

The evidence was kinematic. Later regenerated-beam quantum interference established that the short- and long-lived states reached the same two-pion final state, excluding alternatives such as distinct pion-like particles.^[ref] The 1964 observation established evidence for CP violation; it did not determine every parameter of the CKM matrix. Inferring time-reversal symmetry violation from CP violation invokes CPT symmetry, rather than a direct comparison of time-reversed transitions in that experiment.

The ATLAS experiment and CMS experiment searched proton-proton collisions at the Large Hadron Collider at collision energies of $7$ and $8\mathrm{TeV}$. The ATLAS experiment used silicon tracking, a $2\mathrm{T}$ solenoid, liquid-argon electromagnetic calorimeters and an external muon spectrometer. Its July 2012 paper reported a combined local statistical significance of $6.0$ standard deviations near $126.5\mathrm{GeV}$; this paper result is distinct from the initial 4 July announcement.^[ref]

The CMS experiment used silicon tracking in a $3.8\mathrm{T}$ solenoid, lead-tungstate electromagnetic calorimeters and external muon chambers. Electrons combine tracks and particle showers; muons combine tracking and chamber hits; photons supply shower energies and directions. Selected $H\to \gamma \gamma$ and $H\to Z{Z}^{\ast }\to 4\ell$ candidates, with $\ell =e,\mu$, yielded invariant mass peaks. It checked lepton efficiencies with Z boson decays, estimated fake-lepton backgrounds from control samples with relaxed identification, and fitted the smooth diphoton background from data. Its combined local statistical significance was $5.0$ standard deviations near $125\mathrm{GeV}$.^[ref]

The ATLAS experiment compared signal-plus-background and background-only hypotheses with a profile likelihood, accounting for systematic uncertainties and correlations between decay channels. Diphoton and four-lepton candidates gave precise invariant masses; $W{W}^{\ast }$ decays supplied additional evidence with poorer mass reconstruction because of escaping neutrinos. A local p-value concerns one specified mass; scanning masses requires a look-elsewhere effect correction.^[ref]

Two-photon decay excludes spin one under the usual assumptions, but does not prove spin zero. A mass peak does not determine every Higgs boson coupling. Production rates, branching fractions and angular correlations require additional tests.^[ref]

For a coherently prepared state proportional to $\rho |K_S⟩+|K_L⟩$, evolve each component with ${\lambda }_j=m_j-i{\Gamma }_j/2$. The proper time is $t$, and $\hslash =1$. Since both components reach the same final state, their decay amplitudes add before squaring. Factoring out $|A_S{|}^2$ and a common beam normalization gives the two-pion intensityThe last term is quantum interference. It vanishes upon averaging over an independently random preparation phase, but cannot be discarded from a coherent preparation. Summing the two positive contributions alone would lose the phase-sensitive information.

At late proper time, the short-lived contribution and the quantum interference term die away, leaving the long-lived tail $|{\eta }_{\pi \pi }{|}^2{e}^{-{\Gamma }_{L}t}$. Such a tail is easier to identify after the initially abundant short-lived component has disappeared. The useful experimental balance is between eliminating that component and retaining enough long-lived decays to observe a rare decay channel.

The 1964 report exposed Brookhaven's 80-inch hydrogen bubble chamber to a mass-separated $5.0\mathrm{GeV}/c$ negative-kaon beam. A photographed decay chain, track momenta and bubble density supported the particle identification. Two converted photons helped reconstruct a neutral pion. Alternative assignments were tested kinematically. The authors reported an Omega baryon candidate with $Q=-1$, $S=-3$ and mass $1686\pm 12\mathrm{MeV}/c^2$, reserving a detailed systematic-error discussion for further events.^[ref]

This is an inference from several linked observations. A charged particle can leave a visible bubble-chamber track, while a neutral segment must be reconstructed from its production and decay products. Agreement between possible decay channels, electric charge, momentum conservation and the reconstructed mass is stronger evidence than a suggestive track shape alone. The event tests a predicted hadron pattern; it does not photograph the three strange quarks individually.

For example, an independently constructed two-body kinematic check usesIn a parent rest frame with equal and opposite daughter momenta, the momentum sum vanishes, giving $M{c}^2=E_1+E_2$. In units $c=1$, stipulated daughter masses $m_1=1$, $m_2=1/4$ and momentum magnitude $p=3/4$ give $E_1=5/4$, $E_2=\sqrt{10}/4$ and $M=(5+\sqrt{10})/4\simeq 2.04057$. A common Lorentz boost changes the daughter energies and momenta while preserving this reconstructed invariant mass. These chosen units and numbers are an illustration, not a reanalysis of the 1964 event.

A two-track invariant mass and a direction test answer different questions. In units $c=1$, assign each track the pion mass $m_{\pi }$ and reconstruct its momentum before magnetic deflection. With $p_{\pm }=|{\mathbf{p}}_{\pm }|$ and opening angle $\alpha$,This follows by expanding the squared sum of the two four-momenta. The angle $\theta$ between the reconstructed parent momentum $\mathbf{P}={\mathbf{p}}_{+}+{\mathbf{p}}_{-}$ and the neutral particle beam direction $\hat{\mathbf{n}}$ satisfiesA fully reconstructed two-body decay channel gives the parent mass and $\theta \simeq 0$, within experimental resolution. A three-body decay channel with an unseen neutrino generally misses both constraints; an accidental correct invariant mass alone is insufficient. Notice that the track opening angle $\alpha$ need not be small even when the parent direction angle $\theta$ vanishes.

The 1964 analysis selected $490<M_{\pi \pi }<510$ MeV and remeasured events with $\cos \theta >0.9995$, comparing adjacent mass bands.^[ref]

For an original dimensionless example, take $m_{\pi }=1$, $\hat{\mathbf{n}}=(0,0,1)$ and ${\mathbf{p}}_{\pm }=(\pm \sqrt{3},0,3)$. Each energy is $\sqrt{13}$; the opening angle is $60$ degrees since $\cos \alpha =(9-3)/(9+3)=1/2$. Yet $\mathbf{P}=(0,0,6)$ points exactly along the beam, and $M_{\pi \pi }^2=4(13)-36=16$. Thus a parent of mass $4$ passes both ideal tests. These chosen numbers illustrate four-momentum conservation, not detector performance.